A well known building block toy comprises rectangular pieces made of synthetic resin and having round studs on one side and a recess on the other side shaped so that the studs on one side of a given block may be inserted and frictionally held in the recess on the opposite side of another block. The most well known brand of such building block toys is LEGO. In the building block toy of the prior art described above, the studs are arranged in a basic square pattern and, as a result, the blocks lend themselves readily to being built into rectilinear shapes having right-angled corners.